Oil and gas exploration and production are expensive operations. Knowledge about the formations that can help reduce the unnecessary waste of resources in exploration, well drilling, and production is valuable. Therefore, the oil and gas industry has developed various tools capable of determining and predicting earth formation properties. Nuclear magnetic resonance (NMR) instruments are among the tools utilized by the industry. NMR instruments can be used to determine formation properties, such as the fractional volume of pore space and the fractional volume of mobile fluid filling the pore space. General background of NMR well logging is described in U.S. Pat. No. 6,140,817 issued on Oct. 31, 2000, which is hereby incorporated by reference herein in its entirety.
Nuclear magnetic resonance is a phenomenon occurring in a selected group of nuclei having magnetic nuclear moments, i.e., non-zero spin quantum numbers. When these nuclei are placed in a magnetic field (B0, “Zeeman field”), they precess around the axis of the B0 field with a specific frequency, the Larmor frequency (ω0), which is a characteristic property of each nuclear species (gyromagnetic ratio, γ) and depends on the magnetic field strength (B0) effective at the location of the nucleus, i.e., ω0=γB0.
A proton (1H) is the major nucleus of investigation in well logging NMR applications because of its good NMR sensitivity and its high abundance in water and hydrocarbons. However, other nuclei, such as carbon (13C isotope only, with a natural abundance of 1.1%) also provide NMR signals which can be used to obtain additional information about the sample. In NMR applications, proton and carbon chemical shift and J-coupling spectroscopic techniques may be used to determine molecular structures. Chemical shift is the term given to describe the screening effect of the electrons to the magnetic field that a nucleus experiences. Different chemical groups, such as CH2 and CH3, have different magnitude of screening effects, and, therefore, they appear as separate peaks in the proton chemical shift spectrum. The separation in frequency of different peaks is proportional to the static magnetic field strength, i.e., magnetic field dependent. On the other hand, J-coupling, which is also known as spin-spin or scalar coupling, originates from spin interaction between nuclei through bonding electrons and does not depend on the static magnetic field strength. See, E. L. Hahn, and D. E. Maxwell, Spin echo measurements of nuclear spin coupling in molecules, Physical Review 88, 1070-1084 (1952).
The use of J-editing NMR measurements is disclosed in co-owned U.S. Pat. No. 6,958,604 issued on Oct. 25, 2005 to An et al., which is hereby incorporated by reference herein in its entirety. As disclosed in An et al., one method for obtaining nuclear magnetic resonance measurements includes inducing a static magnetic field in a formation fluid sample, applying an oscillating magnetic field to the fluid sample according to a preparation pulse sequence that comprises a J-edit pulse sequence for developing J modulation, and acquiring the nuclear magnetic resonance measurements using a detection sequence, wherein the detection sequence comprises at least one 180-degree pulse. The method may further include acquiring the nuclear magnetic resonance measurements a plurality of times each with a different value in a variable delay in the J-edit pulse sequence, and analyzing amplitudes of the plurality of nuclear magnetic resonance measurements as a function of the variable delay to provide J coupling information.
The “Fermi contact mechanism” is generally considered to be responsible for J-coupling between nuclear spins. It relies on the fact that an electron in a chemical bond X—Y spends a certain amount of time at the same point in space as, say, nucleus X. In other words, the hybrid orbital (wave function describing the bonded electron) has non-zero amplitude at that location. Thus, if nucleus X has a spin Iz=+1/2, the Pauli exclusion principle results in the electron spin being −1/2. The principle also has two more effects. First, the second bonding electron must have spin +1/2. Second, nucleus Y can only occupy the same point in space as the second bonding electron if its spin is Iz=−1/2. The net effect is that whenever nucleus X has spin +1/2, it is slightly more energetically favorable for nucleus Y to have spin −1/2. The two nuclei are then said to have a positive one-bond J-coupling constant. The coupling mechanism can extend over multiple bonds, although it weakens rapidly as the number of bonds increases.
Isotropic J-coupling is not averaged out by molecular motion, since it relies on bonding electrons. Hence it is also known as scalar coupling. Some interesting properties of J-coupling can be derived from hybrid orbital theory. Hybrid orbitals are formed when several atomic orbitals mix together during the formation of molecules. For example, only electrons in s-type atomic orbitals can contribute to the Fermi contact mechanism, since p-orbitals have zero amplitude (nodes) at the locations of nuclei. Thus the J-coupling strength increases as the s-character of the bond increases. In fact, it depends on the product of the s-characters of the hybrid orbitals from both nuclei that form the bond. It is also proportional to the product of the gyromagnetic ratios of the two bonded nuclei.
Considering 1H—13C one-bond couplings, the proton binding orbital is derived from a single 1s orbital and has a 100% s character. However the carbon binding orbital is derived from one s-type (2s) and three p-type (2px, 2py, and 2pz) orbitals, and can be hybridized in different ways depending on the molecule, such as sp3 (25% s), sp2 (33% s), and sp (50% s). It has been empirically found that in many organic molecules the single-bond 1H—13C J-coupling strength is linearly proportional to the fraction of s-character in the bond:J(C—H)[Hz]≈5[% s(C—H)]  (1)This simple rule predicts J-coupling values of simple non-polar molecules quite well, as shown in Table 1 below:
TABLE 1MoleculeHybridizationPredicted (Hz)Measured (Hz)Methanesp3125125Ethylenesp2165157Benzenesp2165159Acetylenesp250249Aromatic and double-bonded groups have similar properties because the carbon atom is sp2 hybridized in both cases. Additional complications occur for polar molecules. For example, methanol has a single-bond H—C J-coupling frequency of 141 Hz (the J-coupling energy and J-coupling frequency being related by Planck's constant, as is well-known, with the terms being used interchangeably), which is in between the expected values for sp3 and sp2 hybridization. Overall, single-bond 1H—13C coupling strengths range between 100 Hz and 320 Hz.
C—H J-coupling in hydrocarbons only affects those atoms bound to 13C, i.e., approximately 1.1% of the total proton signal. It consists of components at several frequencies. The dominant component at a coupling frequency of 125 Hz corresponds to protons attached to single-bonded carbon atoms, which are sp3-hybridized. Smaller components around 157 Hz correspond to protons attached to aromatic rings and terminal double bonds, which are sp2-hybridized. These values are very similar to the prototypical sp3 and sp2 hybridized molecules shown in Table 1.